First-Order System Least Squares Finite-Elements for Singularly Perturbed Reaction-Diffusion Equations

Autor:	James H. Adler, Scott MacLachlan, Niall Madden
Rok vydání:	2020
Předmět:	Discretization 010103 numerical & computational mathematics First order system 01 natural sciences Finite element method 010101 applied mathematics Norm (mathematics) Reaction–diffusion system Piecewise A priori and a posteriori Applied mathematics Polygon mesh 0101 mathematics Mathematics
Zdroj:	Large-Scale Scientific Computing ISBN: 9783030410315 LSSC
DOI:	10.1007/978-3-030-41032-2_1
Popis:	We propose a new first-order-system least squares (FOSLS) finite-element discretization for singularly perturbed reaction-diffusion equations. Solutions to such problems feature layer phenomena, and are ubiquitous in many areas of applied mathematics and modelling. There is a long history of the development of specialized numerical schemes for their accurate numerical approximation. We follow a well-established practice of employing a priori layer-adapted meshes, but with a novel finite-element method that yields a symmetric formulation while also inducing a so-called “balanced” norm. We prove continuity and coercivity of the FOSLS weak form, present a suitable piecewise uniform mesh, and report on the results of numerical experiments that demonstrate the accuracy and robustness of the method.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::e29be4d1ce22c2ae6db2066e570165ed https://doi.org/10.1007/978-3-030-41032-2_1 Zobrazit plný text záznamu